Solve for $z$, $ \dfrac{1}{10z - 6} = \dfrac{5}{10z - 6} - \dfrac{3z + 7}{10z - 6} $
Explanation: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $10z - 6$ $10z - 6$ and $10z - 6$ The common denominator is $10z - 6$ The denominator of the first term is already $10z - 6$ , so we don't need to change it. The denominator of the second term is already $10z - 6$ , so we don't need to change it. The denominator of the third term is already $10z - 6$ , so we don't need to change it. This give us: $ \dfrac{1}{10z - 6} = \dfrac{5}{10z - 6} - \dfrac{3z + 7}{10z - 6} $ If we multiply both sides of the equation by $10z - 6$ , we get: $ 1 = 5 - 3z - 7$ $ 1 = -3z - 2$ $ 3 = -3z $ $ z = -1$